I don't know the technical name for it, but it's a vacuum operated valve. When you turn your AC on max setting, vacuum is used to close the valve and prevent coolant from entering the heater core so you will have cooler AC.
You can either replace it or get a piece of pipe in its place. If you decide to go with the cheap pipe fix, you need to cap off the gray vacuum line so you don't have a vacuum leak. Lucky for us, for supplied a nipple for those who didn't have the heater valve.
The nipple is on the HVAC box. In this picture, below my finger you will see the gray vacuum line connected to the nipple. I don't use AC too much so I removed my valve in place for the coolant filter connection.